Gravitational self-force by mode sum regularization - art. no. 084021

Authors
Citation
L. Barack, Gravitational self-force by mode sum regularization - art. no. 084021, PHYS REV D, 6408(8), 2001, pp. 4021
Citations number
30
Categorie Soggetti
Physics
Journal title
PHYSICAL REVIEW D
ISSN journal
05562821 → ACNP
Volume
6408
Issue
8
Year of publication
2001
Database
ISI
SICI code
0556-2821(20011015)6408:8<4021:GSBMSR>2.0.ZU;2-O
Abstract
We propose a practical scheme for calculating the local gravitational self- force experienced by a test mass particle moving in a black hole spacetime. The method-equally effective for either weak or strong field orbits-employ s the mode-sum regularization scheme previously developed for a scalar toy model. The starting point for the calculation. in this approach, is the for mal expression for the regularized self-force derived by Mino et al. [Phys. Rev. D 55, 3457 (1997)] (and, independently, by Quinn and Wald [Phys. Rev. D 56 3381 (1997)]), which involves a worldline integral over the tail part of the retarded Green's function. This force is decomposed into multipole (tensor harmonic) modes. whose sum is subjected to a carefully designed reg ularization procedure. This procedure involves an analytical derivation of certain "regularization parameters" by means of a local analysis of the Gre en's function. This paper contains the following main parts: (1) The introd uction of the mode sum scheme as applied to the gravitational case. (2) Two simple cases studied: the test case of a static particle in flat spacetime , and the case of a particle at a turning point of a radial geodesic in Sch warzschild spacetime. In both cases we derive all necessary regularization parameters. (3) An analytical foundation is set for applying the scheme in more general cases. (In this paper, the mode sum scheme is formulated withi n the harmonic gauge. The implementation of the scheme in other gauges shal l be discussed in a separate. forthcoming paper.).